Problem Set & Assignment : The Aftermath

Unfortunately, I couldn't do the LOG(refer to my last post) for the following reasons:
1) My computer had to be close.
2) I rather write than type.
3) Laziness.

Problem set #4 was pretty straightforward. My only problem approaching it was the flavor of induction. I used complete induction because it felt more safe based on its definition. I usually use complete induction when I can't get from P(n) to P(n+1). However, for this question we can get from P(n) to P(n+1). So my problem was with the fact that there were two base cases(Namely, P(0) and P(1)) where in the definition of simple induction we only verify P(0). So this is my random thought for proving this problem using simple induction:

*Prove P(n) for all n>=1 using the base case P(1)
*Verify P(0) manually
Since there is no natural number between 0 and 1 => P(n) for all n

So basically, my real question is if we can have more than 1 base case for simple induction?

Assignment #2:

#1 - We barely get questions like this. We have all the tools necessary. There's no complicated formal structure. It was a great puzzle and I have to say, although I don't think I got it right, I enjoyed doing it very much and I would happily loose marks for questions like this.
#3 - I enjoyed doing this question very much. Mainly because of the verbal explanation of G(n) which made total sense.
#4 - Very similar to lecture notes and as a result a straightforward question.

...and Happy Halloween!

Problem Sets & Assignments

I missed two days of lectures. Being in the evening section makes it 6 lectures. First one due to sickness and second one due to high load of assignments and midterms. However, I managed to do problem set #3 very easily. I think not knowing what was going on in the lectures actually didn't mislead me to look for something similar to Fibonacci closed form.

I'm far behind and I'm going to dedicate the next two days studying lecture notes, and doing problem set #4 and assignment #2. My next post is going to be in log format showing my progress or rather confusion in these two days.

Term Test # 1

Today we had our first term test. As expected, three proof questions. It was pretty fair and we had enough time.

For some reason, when doing proofs using induction I find my mind looking for a direct mathematical proof instead of an induction proof and I have to remind myself almost every ten seconds that remember that this is a proof using induction. It's as if my mind is working against me. Today, for two of the questions I got carried away looking for a way to "derive" the result instead of trying to "verify" it and spend almost 70% of my time doing so. But, fortunately I got back on track and was able to make it just in time.

And here's this week's lecfun taken from week 5, slide 3:

First Post

I got my SLOG up and running. I know it doesn't sound much but I finally managed to get rid of that horrible looking toolbar at the top.

This week, I decided to investigate the relationship between Fibonacci sequence and the Golden Ratio. I first got interested in Golden Ratio, after I saw "Pi", an independent movie. I have to say out of all the relationships, the formula by Johannes Kepler got my attention the most. It is probably the simplest formula:


He wrote "as 5 is to 8 so is 8 to 13, practically, and as 8 is to 13, so is 13 to 21 almost”*

And one more thing...
Fortunately a "fun" idea for my SLOG hit me today. Being more of a graphic designer than a writer, I'm going to finish my entries for the week by a "lecfun" section. It's a screenshot of lecture notes taken out of context. I hope everyone understands that this is ONLY for fun and I also hope to get the approval from Danny Heap.

*Kepler, Johannes (1966). A New Year Gift: On Hexagonal Snow. Oxford University Press, 92. ISBN 0198581203. Strena seu de Nive Sexangula (1611)